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Spectral Simulation of Isotropic Gaussian Random Fields on a Sphere

Abstract : A spectral algorithm is proposed to simulate an isotropic Gaussian random field on a sphere equipped with a geodesic metric. This algorithm supposes that the angular power spectrum of the covariance function is explicitly known. Direct analytic calculations are performed for exponential and linear covariance functions. In addition, three families of covariance functions are presented where the calculation of the angular power spectrum is simplified (shot-noise random fields, Yadrenko covariance functions and solutions of certain stochastic partial differential equations). Numerous illustrative examples are given.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-02736248
Contributor : Xavier Freulon <>
Submitted on : Tuesday, June 2, 2020 - 5:25:09 PM
Last modification on : Wednesday, March 24, 2021 - 3:56:02 PM

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Christian Lantuéjoul, Xavier Freulon, Didier Renard. Spectral Simulation of Isotropic Gaussian Random Fields on a Sphere. Mathematical Geosciences, Springer Verlag, 2019, 51 (8), pp.999-1020. ⟨10.1007/s11004-019-09799-4⟩. ⟨hal-02736248⟩

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